KABUL — Afghanistan’s Taliban insurgents on Monday said an abducted US professor was gravely ill and urged the United States to accede to their demands for his release and that of an Australian colleague.

Kevin King and Australian Timothy Weeks were taken at gunpoint outside American University in Kabul last year, and later appeared in a January video tearfully asking President Trump to exchange them for militant prisoners.

‘‘We have periodically tried to treat and cure him, but since we are facing a war situation, we do not really have access to health facilities to provide him complete treatment,’’ said Zabiullah Mujahid, a spokesman for the Taliban.

Mujahid said King, 61, has heart disease, kidney problems, and swollen feet, and that the Taliban would hold the US government responsible if he dies.

He said the Taliban had presented to the United States its demands for releasing the pair, but did not reveal what they were.

The US embassy in Kabul said it was aware of the Taliban statement. ‘‘It is appalling that the Taliban continue to take and hold hostages in such dire circumstances,’’ the embassy said.

‘‘We call for the immediate and unconditional release of Kevin King and all other hostages. The US government will never stop trying to recover them and other Americans held by criminal and terrorist networks around the world,’’ it said.

In September 2016, the Pentagon mounted an unsuccessful rescue mission for the hostages.

Washington Post